Optimal control of beer fermentation processes with Lipschitz-constraint on the control
Nowadays, one can find in almost all industrial products a trail of mathematical optimization. In particular, the theory and algorithms of optimal control have helped in various fields to reduce the production time and to improve the quality of the considered products. As a special class of applications, two optimal control formulations for the fermentation process of beer are presented. The reactions of the fermentation processes are modelled by a system of ordinary differential equations that are steered by the heating and cooling of the involved substrates. The occurring physical limitations, such as temperature limits and the requirement to avoid scenarios with unrealistic bang-bang controls, give rise to optimal control problems with general control constraints. Therefore, this paper has reviewed a forward–backward sweeping method for solving these kinds of optimal control problems and presents encouraging numerical results that were obtained by this approach.